That's what I started with... and this year I planted some of my garlic from last year as well as some from the grocer. My rule with the store bought garlic is, it must have some of the roots showing on the garlic bulb. the garlic bulbs you find at the store with the root scooped out... those are from china and I will avoid those.
this is the perfect time of year to plant your garlic here in Tx.. and if you plant by the moon, the 24th, 27th & 28th of Sept. are good days to plant root veggies. Just separate the garlic cloves and plant them point up, with the tip barely showing in the ground. They will grow fine over winter and they are usually ready to pull up around the end of may or first part of june. "they" say the garlic is ready when the green tops fall over and die.. but I haven't found that to be true of garlic, that's for onions; although the outer greens of the garlic will start to brown and fall when they're ready.
They grow well in most soils but don't add any manures or heavy fertilizer, it can cause rotting. Mine grow really well in clay soil that has been minimally improved.
I've never kept my garlic in the ground long enough to see if it will spread and reproduce - yet!!